A004701 Expansion of e.g.f. 1/(4 - exp(x) - exp(2*x) - exp(3*x)).

1, 6, 86, 1836, 52250, 1858716, 79345346, 3951633636, 224917803770, 14402023566156, 1024662142371506, 80191908540219636, 6846505625682597290, 633241684193651067996, 63074628985206471485666, 6731364953866743063784836

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Column k=3 of A320253.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(4-Exp(x)-Exp(2*x)-Exp(3*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Oct 09 2018

Maple

seq(coeff(series(factorial(n)*(4-exp(x)-exp(2*x)-exp(3*x))^(-1),x,n+1), x, n), n = 0 .. 15); # Muniru A Asiru, Oct 10 2018

Mathematica

With[{nn=20},CoefficientList[Series[1/(4-Exp[x]-Exp[2*x]-Exp[3*x]),{x,0,nn}],x] Range[0,nn]!] (* Vincenzo Librandi, Jun 14 2012 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(4-sum(k=1,3, exp(k*x))))) \\ G. C. Greubel, Oct 09 2018

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (1 + 2^k + 3^k) * a(n-k). - Ilya Gutkovskiy, Jan 15 2020